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Item type:Publication, Access status: without files , Sample Complexity of Device-Independently Certified "quantum Supremacy"(2019-05-29); ; ; Results on the hardness of approximate sampling are seen as important stepping stones toward a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include boson sampling, instantaneous quantum polynomial time (IQP) circuit sampling, and universal random circuit sampling. A key challenge for any such demonstration is to certify the correct implementation. For all these examples, and in fact for all sufficiently flat distributions, we show that any noninteractive certification from classical samples and a description of the target distribution requires exponentially many uses of the device. Our proofs rely on the same property that is a central ingredient for the approximate hardness results, namely, that the sampling distributions, as random variables depending on the random unitaries defining the problem instances, have small second moments.Publicationtype: Journal ArticleScopus© Citations 22 26 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Direct certification of a class of quantum simulations(2017-03-01); ; ; One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. Important cases are situations in which one cannot classically calculate local expectation values of state preparations efficiently. In this work, we develop weak-membership formulations of the certification of ground state preparations. We provide a non-interactive protocol for certifying ground states of frustration-free Hamiltonians based on simple energy measurements of local Hamiltonian terms. This certification protocol can be applied to classically intractable analog quantum simulations: For example, using Feynman-Kitaev Hamiltonians, one can encode universal quantum computation in such ground states. Moreover, our certification protocol is applicable to ground state encodings of IQP circuits aiming at the demonstration of quantum supremacy. These can be certified efficiently when the error is polynomially bounded.Publicationtype: Journal Article9